An example of a Kubo–Martin–Schwinger state for a nonlinear classical poisson system with infinite-dimensional phase space

A “smoothed” nonlinear Klein–Gordon equation is regarded as the equation of evolution of a classical dynamical system with an infinite-dimensional phase space. It is proved that the wave operators are canonical transformations of this system that linearize it. It is shown that a Gaussian measure induces a Kubo–Martin–Schwinger state for the linear system, and that the preimage of this measure under the canonical transformation implemented by a wave operator is a Kubo–Martin–Schwinger state for the original nonlinear system.
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